Can't Update iPhoto because it is not available in the App Store
If you didn't update your 9.x version of iPhoto prior to updating OS X Yosemite to 10.10.3, you cannot update the app through the App Store. Support for iPhoto was dropped with the release of Photos in Yosemite 10.10.3.
While you still cannot update iPhoto, you can re-install the app which will download the current version.
Note that you must have some version of iPhoto 9.x for this to work. If you never purchased the 9.x version of iPhoto, you will not be able to update it to the Yosemite version.
First, go to the App Store, Purchases tab, and make sure iPhoto is in the list of purchased software. It may be hidden, so check for that: Hide and unhide purchases in the Mac App Store - Apple Support.If it is not in your Purchases list, this will not work, so don't bother continuing.
Just as a precaution, copy iPhoto from your Applications folder onto an external disk or USB stick and eject that drive.
Move iPhoto from your Applications folder into the Trash. Make sure there are no disks mounted that have a copy of the iPhoto app on them before going to the App Store.
Make sure no other users have iPhoto open in the background. It is best to have all other users logged out.
I ended up having to Restart before I could clear iPhoto from the App Store memory (it was still showing Update on the button in Purchases).
If it is still showing as Update, try searching Spotlight for iPhoto. There may be a copy on a mounted external disk that it is identifying.
You should now be able to go to the Purchases tab and find iPhoto with the Update button labeled "Install"
Click "Install" and it should download the current version which works with Yosemite.
When I first tried, after authenticating, it posted a 503 error and asked if I wanted to Retry. When I clicked "Retry," it started downloading.
It's about 1.2 GB, so it takes a little while to fully download.
*Updated to address Hidden Purchases as pointed out by sberman
*Change the title to reflect common search terms and incorporateted OT's suggestion.